[Aethaeryn]

    The whole point of taxes is that we can't rely on voluntary
    donations to fund public goods.

Actually, the Romans did just that.

https://en.wikipedia.org/wiki/Aedile

Note this part from the article in particular:

    Because Aediles were not reimbursed for any of their public
    expenditures, most individuals who sought the office were
    independently wealthy. Since this office was a stepping stone to
    higher office and the Senate, it helped to ensure that only
    wealthy individuals (mostly landowners) would win election to
    high office.

So, yes, it's possible to organize things that way, but the side effect is that it limits political power and offices to those who are wealthy. And, yes, the Romans also had taxes so they didn't rely on this method entirely, but this is an alternative model of funding public expenses without taxation and hence a counterexample to your claim.

On the other hand, there's a lot of money that is being spent on campaign advertisements. Perhaps it would be a net gain for society if politicians 'advertised' by spending that cash on public goods instead. Perhaps we can learn from the Romans. :-P